Final answer:
The current as a function of time, i(t), for a capacitor where v(t) = √t + 1 is calculated by finding the derivative of v(t) which is 1/(2√t), and multiplying it by the capacitance (10μF).
Step-by-step explanation:
The equation for current as a function of time, i(t), for a capacitor with a voltage v(t) can be determined by differentiating the voltage function with respect to time and then dividing by the resistance, as per the relationship i(t) = C dv/dt where C is the capacitance.
Given that v(t) = √t + 1 and the capacitance is 10μF, we first find the derivative of v(t), which is dv/dt = 1/(2√t). Then, we multiply this derivative by the capacitance to find i(t). As there is no resistance provided in the question, we would assume a series resistance of 0, which is not practical. However, for the purpose of the question, the current as a function of time, using only the given information, can be represented as i(t) = (10μF) × 1/(2√t).